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Axiom ax-11 1336
Description: Axiom of Variable Substitution. One of the 5 equality axioms of predicate calculus. The final consequent is a way of expressing " substituted for in wff " (cf. sb6 1686). It is based on Lemma 16 of [Tarski] p. 70 and Axiom C8 of [Monk2] p. 105, from which it can be proved by cases.

Variants of this axiom which are equivalent in classical logic but which have not been shown to be equivalent for intuitionistic logic are ax11v 1629, ax11v2 1622 and ax-11o 1625. (Contributed by NM, 5-Aug-1993.)

Assertion
Ref Expression
ax-11

Detailed syntax breakdown of Axiom ax-11
StepHypRef Expression
1 vx . . 3
2 vy . . 3
31, 2weq 1331 . 2
4 wph . . . 4
54, 2wal 1272 . . 3
63, 4wi 4 . . . 4
76, 1wal 1272 . . 3
85, 7wi 4 . 2
93, 8wi 4 1
Colors of variables: wff set class
This axiom is referenced by:  ax10o  1525  equs5a  1596  sbcof2  1612  ax11o  1624  ax11v  1629
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